Time-dependent characteristics of two-layer functionally graded plates adhesively bonded by a viscoelastic interlayer based on Kirchhoff plate theory

Abstract

An analytical solution is proposed to investigate the time-dependent characteristics of two-layer functionally graded plates with a viscoelastic interlayer. The elastic modulus in each graded layer varies through the thickness following an arbitrary function, and its mechanical properties are described based on the Kirchhoff theory. The Maxwell-Wiechert model is applied to simulate the viscoelastic adhesive interlayer with the neglect of memory effect. The energy equation of the system is expressed by the deformation components, which are expanded as the double trigonometric series. By virtue of variational method, the solutions of stress and deformation are determined efficiently. The comparison study indicates that the present solution matches the finite element solution well; however, the finite element method is highly time-consuming because of the fine mesh in the geometric shape and the time step. Finally, the influences of the geometry and material on the time-dependent behavior of the structure are discussed in detail.